Illegal content on social media poses significant societal harm and necessitates timely removal. However, the impact of the speed of content removal on prevalence, reach, and exposure to illegal content remains underexplored. This study examines the relationship with a systematic audit of takedown delays using data from the EU Digital Services Act Transparency Database, covering five major platforms over a one-year period. We find substantial variation in takedown delay, with some content remaining online for weeks or even months. To evaluate how these delays affect the prevalence and reach of illegal content and exposure to it, we develop an agent-based model and calibrate it to empirical data. We simulate illegal content diffusion, revealing that rapid takedown (within hours) significantly reduces prevalence, reach, and exposure to illegal content, while the longer delays measured by the audit fail to reduce its spread. Though the link between delay and spread is intuitive, our simulations quantify exactly how takedown speed shapes exposure to illegal content. Building on these results, we point to the benefits of faster content removal to effectively curb the spread of illegal content, while also considering the limitations of strict enforcement policies.